Continuous random alloy networks: Glass transition and elasticity

Amorphous alloys can be modelled as random networks of atoms or molecules of differing valencies. A statistical-mechanical theory of such networks is presented for the case of binary amorphous alloys. The existence of a continuous equilibrium phase transition, from the liquid state to the amorphous solid state driven by increasing the density of permanent random covalent bonds, is demonstrated. The structural and elastic properties of the amorphous solid state are calculated through the use of a variational Ansatz, and a discussion is given of the dependence of these properties on the relative concentration of the constituent atoms or molecules and their valencies. Implications of the present results in the context of gelation are addressed, especially with regard to the (primarily entropic) elastic properties of gels.